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Stratified and Cluster Sampling
Chapter 16
Stratified Sample
A probability sample in which:
• The parent population is divided into
mutually exclusive and exhaustive
subsets
• A simple random sample of elements is
chosen INDEPENDENTLY FROM each
group or subject
SLIDE 16-1
Some Characteristics of Stratified
Samples
• Why used
Can produce sample statistics that are more precise or
which have smaller sampling error
Allows the investigation of the characteristics of interest
for particular subgroups since one can ensure adequate
representation from each subgroup of interest
• Issues
What criteria should be used to stratify the population of
interest?
How many strata should we have?
Should we use
•Proportionate stratified sampling, or
•Disproportionate stratified sampling
SLIDE 16-2
Quantities Needed to Establish a Confidence
Interval for a Population Mean With a Stratified
Sample
• A decision as to the degree of confidence
desired
• A point estimate of the population mean
• An estimate of the sampling error associated
with this statistic
How might you get each of these?
SLIDE 16-3
Example Calculations for Generating a
Confidence Interval with a Stratified Sample
I
II
n1 = 100
x1 =
^
s12 =
 Xi1
n2 = 100
= 3.2
x2 =
 (Xi1 x1 )2
= .14
n1-1
^
s22 =
n1
III
^
s32 =
 Xi3
= 4.6
 (Xi2 x2 )2
= .12
n2-1
n4 = 100
= 5.8
x4 =
 (Xi3 x3 )2
= .20
n3-1
^
s42 =
n3
n2
IV
n3 = 100
x3 =
 Xi2
 Xi4
n4
= 7.2
 (Xi4 x4 )2
= .18
n4-1
SLIDE 16-4
Size of Strata in Parent Population
I.
N1 =
5000
II.
N2 =
25000
III.
N3 =
15000
IV.
N4 =
5000
N = 50000
L
xst

h=1
=
Whxh
Nhxh

h=1
L
=
N
= 1/10(3.2) + 5/10(4.6) + 3/10(5.8) + 1/10(7.2) = 5.08
2
L
sx2st =

h=1
Whs2xh
L
=

h=1
Nh
^ )2
(s
h
N
nh
( )
= (1/10)2 (.14) + (5/10)2 (.12) + (3/10)2 (.20)
100
100
100
+ (1/10)2 (.18) = .000512
100
sxst =.0226
SLIDE 16-5
Cluster Sample
A probability sample in which:
• The parent population is divided into mutually
exclusive and exhaustive subsets
• A random sample OF subsets is chosen
SLIDE 16-6
Target Population of Companies in City
Company
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
Location of Allows Flexible
Company
Schedules
Yes
West
No
South
Yes
East
Yes
West
No
West
No
North
No
West
Yes
South
Yes
North
No
North
No
East
Yes
South
No
West
Yes
West
Yes
East
No
North
No
South
No
North
No
East
No
East
Company
U
V
W
X
Y
Z
AA
BB
CC
DD
EE
FF
GG
HH
II
JJ
KK
LL
MM
NN
Location of Allows Flexible
Company
Schedules
Yes
West
No
West
No
North
No
South
Yes
West
Yes
East
No
West
No
South
Yes
West
Yes
East
No
North
No
West
No
West
No
North
No
South
No
North
Yes
East
No
West
Yes
West
No
North
SLIDE 16-7
Statistical Efficiency
A relative notion used to compare sampling
plans. One sampling plan is more statistically
efficient than another if, FOR THE SAME SIZE
SAMPLE, it produces a smaller standard error
of estimate.
SLIDE 16-8
Systematic Sample
A form of cluster sampling in which every kth element
in the population is designated for inclusion in the
sample after a random start.
Procedure to draw:
•
•
•
•
•
Determine the sample size n
Determine the sampling fraction f =
population size
n
N
where n is the
Determine the sampling interval i = 1/f
Generate a random start between 1 and i using a random
number table
Use the randomly determined element and every ith
element thereafter for the sample
SLIDE 16-9
Area Sample
A form of cluster sampling in which areas (for
example, census tracks, blocks) serve as the
primary sampling units. The population is divided
into mutually exclusive and exhaustive areas
using maps and a random sample of areas is
selected. If:
• All the households in the selected areas are
used in the study, it is one-stage area sampling
• If the areas themselves are sampled with
respect to households, it is two-stage area
sampling.
SLIDE 16-10
Illustration of Area Sample
• Suppose 5 blocks are to be
selected and suppose a
random number table
indicates blocks 2, 8, 19,
31, and 39 are to be used
• If all of the households
within these blocks are
contacted, it is one-stage
area sampling
• If a sample of households
is selected from each of
these blocks, it is twostage area sampling
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32
33 34 35 36 37 38 39 40
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32
33 34 35 36 37 38 39 40
SLIDE 16-11
Types of Two-Stage Area Samples
• Simple
 A certain proportion of second-stage units
(e.g., households) is selected from each firststage unit (e.g., block)
• Probability-proportional-to-size
 A fixed number of second-stage units (e.g.,
households) is selected from each first-stage
unit (e.g., block) but the probability of each
first-stage unit being chosen is directly
related to its size
SLIDE 16-12